### Research group:

Small retractions onto trees

- Cauty's solution of an old famous Knaster's problem

#### 20 - 24 September, 2011, Warsaw

### Organizer

- R. Mańka (with assistance of J. Krasinkiewicz)

### Participants

- R. Cauty (Université Paris 6)
- J. Krasinkiewicz (IMPAN)
- R. Mańka (IMPAN)
- M. Sobolewski ( Institute of Mathematics of the University of Warsaw)<

### Programme

During these meetings professor Robert
Cauty presented his proof of the following theorem which resolves
in the positive a long-standing famous problem of B. Knaster
(posed in 1957):

*For any dendroid X and e > 0 every tree in X extends to a
tree which is an e-retract of X.
*This theorem is deep and very important, its proof is long and
extremely difficult. As far as we know, no one till now (except
possibly the author himself) was able to comprehend it.

Our meetings were held at the Institute of Mathematics of the Polish Academy of Sciences, 8 Śniadeckich street, and lasted from 11:00 a.m. till 06:00 p.m. everyday (September 21,22 and 23). In spite of this, we still have many questions to be asked and do not understand some ideas of the proof.